Answer:
$8,500 in CDs; $11,500 in bonds
Step-by-step explanation:
Let c = amount invested in CDs.
Let b = amount invested in bonds.
"A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CDs)."
From the total investment, we get this equation.
c + b = 20000
"If the amount invested in bonds is to exceed that in CDs by $3000"
From the details of the amounts, we get this equation.
b = c + 3000
We have a system of equations in two unknowns.
c + b = 20000 Eq. 1
b = c + 3000 Eq. 2
Since Eq. 2 is already solved for b, we will use the substitution method to solve the system of equations.
Substitute b in Eq. 1 with c + 3000.
c + c + 3000 = 20000
2c + 3000 = 20000
2c = 17000
c = 8500
Now substitute c = 8500 in Eq. 2 and solve for b.
b = c + 3000
b = 8500 + 3000
b = 11500
Answer: $8,500 in CDs; $11,500 in bonds
The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.
1= 0.411
2=0.278
3=0.221
4=0.080
5=0.010
(a) Find the mean, variance and standard deviation of the probability distribution.
(b) Interpret the results: A, B, C or D.
A. The average hurricane is aprox. category 1.
B. The average hurricane is aprox. category 2.*
C. Most of the hurricane sizes differ from the average by about 2 or 3.
D. Most of the hurricane sized differ from the average by about 1 or 2.*
Answer:
a) mean = 0.2
variance = 0.0391
standard deviation = 0.198
b) The average hurricane is aprox. category 2.* (B)
Step-by-step explanation:
In order to find the mean, variance, and standard deviation, let us for a table for the data:
level x
1 0.411
2 0.278
3 0.221
4 0.080
5 0.010
Calculating the mean ([tex]\bar{x}[/tex])
[tex]\bar{x} = \frac{x_1+x_2+x_3+x_4 + x_5}{n}\\\\\bar{x} = \frac{0.411 + 0.278 + 0.221 + 0.080 + 0.010}{5}\\\bar{x} = \frac{1}{5}\\ \bar{x} = 0.2[/tex]
∴Mean = 0.2
level x [tex]x- \bar{x}[/tex] [tex](x - \bar{x})^2[/tex]
1 0.411 0.211 0.0445
2 0.278 0.078 0.0608
3 0.221 0.021 0.000441
4 0.080 -0.12 0.0144
5 0.010 -0.19 0.0361
[tex]\sum(x - \bar{x})^2 = 0.1562[/tex]
[tex]variance = \frac{\sum(x - \bar{x})^2}{n-1} \\variance = \frac{0.1562}{4} \\variance = 0.0391[/tex]
standard deviation = √(variance)
Standard deviation = √(0.0391)
Standard deviation = 0.198
b) the average hurricane is aprox. category 2 (B)
Susan borrows $4500 from the bank to purchase new furniture. The bank finances for 5 years at 8% simple interest. How much will Susan pay for the furniture. (I = Prt) (A = I + P) PLS HELP ME I HAVE TO TURN THIS IN SOON!!!!!!!!!!!!!!!!!!!
Answer:
$6300
Step-by-step explanation:
A = P(1 + rt)
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
t = Time Period involved in months or years
P = $4500
t = 5 years
r = 8% = .08
A = P(1 + rt)
A = 4500 ( 1 + (.08*5))
A = 4500 ( 1 + .4)
A = 4500 (1.4)
A = $6300
Susan will pay $6300 for the furniture
________________________________________________________
The equation I used is the same as what you were given:
I = Prt
A = I + P Re-write as I = A - P
So you plug in A - P for I:
A - P = Prt Add P to each side
A - P + P = Prt + P
A = Prt + P Pull P out
A = P(rt + 1) Re-arrange
A = P(1 + rt)
Same equation!
What is the cumulative area from the left under the curve for a z-score of -0.875? What is the area on the right of that z-score?
please explain why for each step and excel formula
Answer:which z sqore are u talking about
Step-by-step explanation:
The sum of twice a number n and 8 is at most 5
Answer:
n is less than or equal to -1.5
Step-by-step explanation:
2n+8 is less than or equal to 5.
2n is less than or equal to -3
n is less than or equal to -1.5
Answer:
n is less than or equal tn is less than or equal to -1.5
Step-by-step explanation:
so it would be 2n + 8 ≤ 5 and 2n + 8 ≤ 5
hope this helped!
p.s it would be cool if you gave me brainliest
What is 8.5+ 3.4 - 6.5 - (-1.6) = ?
Indicate which property is illustrated in Step 2
7 + (1 + 7) + 0 = 7+ (7 + 1) + 0
= (7 + 7) + (1 + 0)
= (7 + 7) + 1
= 14 +1
Step 1
Step 2
Step 3
Step 4
OA. commutative property of multiplication
OB. identity property of addition
oc. distributive property
OD. associative property of addition
Answer:
the associative property of addition i think
Step-by-step explanation:
90% of runners in a marathon successfully completed it. 30% of these runners were men. How many total runners began the marathon if 270 men completed it?
Answer:
1000
Step-by-step explanation:
270 is 30% of 900 total who completed.
900 is 90% of 1000
natalie budgets $150 for yoga training but doesn’t want to spend all of that money. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of day,d, that Natalie can take classes and stay under (less than) her budget?
Answer:
A
Step-by-step explanation:
Answer:
A) I hope I helped you ◉‿◉
The difference between two positive integers is 6. If the smaller is added to the square of the larger, the sum is 84. Find the integers.
Answer:
Step-by-step explanation:
B
A metal bar has the D of 7.9 g/mL. If the volume of the bar is 500mL, what is the mass in kg?
The density of a substance is the mass per unit volume. The mass of the metal bar is 3.95 kg.
What is density?The density of a substance is the mass per unit volume.
It can be given as,
[tex]\rho=\dfrac{m}{v}[/tex]
Here, [tex]m[/tex] is the mass of the substance and [tex]v[/tex] is the volume of hte substance.
Given information
A metal bar has the D of 7.9 g/mL .
Volume of the bar is 500 mili liter.
Suppose the mass of the metal bar is [tex]m[/tex] grams. Thus put the values in the above formula as,
[tex]\rho=\dfrac{m}{v}\\7.9=\dfrac{m}{500}\\[/tex]
Solve for m,
[tex]m=500\times7.9\\m=3950[/tex]
Thus the mass of the metal bar is 3950 grams. Convert it into the kg as divide by 1000. Thus,
[tex]m=\dfrac{3950}{1000}\\m=3.950[/tex]
Hence the mass of the metal bar is 3.95 kg.
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The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?
The length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.
Given that a hydrogen atom has about 1.04 × 10⁻¹⁰ meters diameter, whereas a protein molecule has an overall length of 2 × 10³ times the diameter of a hydrogen atom.
We need to find the length of the protein molecule, in meters and in scientific notation.
We must multiply the diameter of a hydrogen atom by the specified factor (2 × 10³), in order to determine the length of the protein molecule in meters.
Let's compute the amount:
Length of protein molecule = Diameter of a hydrogen atom × 2 × 10³
Diameter of a hydrogen atom = 1.04 × 10⁻¹⁰ meters
Length of protein molecule = 1.04 × 10⁻¹⁰ meters × 2 × 10³
To multiply numbers in scientific notation, we add the exponents and multiply the coefficients:
Length of protein molecule = 2.08 × 10⁻⁷ meters
So, the length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.
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The length of the protein molecule, in meters and written in scientific notation, is approximately 2.08 × 10^(-7) meters.
To calculate the length of the protein molecule in meters, we'll start with the given diameter of a hydrogen atom and multiply it by the scaling factor of 2000. Let's perform the calculations:
Diameter of a hydrogen atom = 1.04 × 10^(-10) meters
Length of the protein molecule = 2000 × (Diameter of a hydrogen atom)
Multiplying the diameter by the scaling factor:
Length of the protein molecule = 2000 × (1.04 × 10^(-10))
When multiplying numbers written in scientific notation, we can multiply the coefficients and add the exponents:
Length of the protein molecule = 2000 × 1.04 × 10^(-10)
Calculating the coefficient:
2000 × 1.04 = 2080
Calculating the exponent:
10^(-10)
Putting the coefficient and exponent together:
Length of the protein molecule = 2080 × 10^(-10)
Writing it in scientific notation:
Length of the protein molecule = 2.08 × 10^(-7)
for such more question on length
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Select all the partial products for
9
×
813
.
A.
12
B.
27
C.
90
D.
900
Answer:
ok639010 is the answer of the day when I am in the toilet
can someone please help me :)
Answer:
30
Step-by-step explanation:
RST=RSV-TSV
2x+8=11x+10-101
2x-11x=10-8-101
-9x=-99
x=99/9
x=11
--->RST=2(11)+8
RST=30
Help please thanks :)
Answer:No Solution
Step-by-step explanation:
Consistent dependent like 0=0 or x=x
The algebra tiles represent the perfect square trinomial x2 + 10x + c.
What is the value of c?
c =
Personal Finance: Cost of a Car The suggested list price of a new car is $24,000. The dealer’s cost is 85% of list. How much will you pay if the dealer is willing to accept $300 over cost for the car?
Answer: $20,700
Step-by-step explanation:
Given that :
List price of car = $24,000
Dealer's cost = 85% of the list price of the car
Dealer acceptance cost = $300 over the cost
Hence, total amount to be paid :
Dealer's cost + dealer's acceptance cost
Dealer's cost = (0.85 * $24,000) = $21,400
Hence, Total cost :
$20,400 + $300 = $20,700
Day 2- Real World- Midpoint
While planning the layout of her yard, Laura created a grid
system representing her backyard. On the grid, Laura placed
the center of a herb garden at the coordinates (3.14) and wants
to place a bird bath at the point (7,29). If Laura wants to
position the center of a flower garden so that the bird bath is
halfway between the herb and flower gardens, at what
coordinates should the center of the flower garden be placed?
(11, 150
O (11,44)
O (4,44)
O (4,15)
Help
Answer:
Point of the flower garden R ( 11, 44 )
Step-by-step explanation:
Let´s call P ( 3, 14 ) The center of the herb garden, and Q ( 7 , 29 ) the birdbath point
Differences in coordinates of these two points are:
x axis 7 - 3 = 4
y axis 29 - 14 = 15
Then the point Q ( x , y ) will be at: Q ( 11, 44)
x axis x = 11 because 7 + 4 = 11 means that the coordinate 7 is just halfway way between coordinates (x) 3 and 11 ( 4 above 3, and 4 below 11)
Reasoning the same way we conclude y = 44 in this case 29 is just halfway between coordinates (y) 14 and 44 ( 15 above 14 and 15 below 44)
We can probe getting distance d₁ between P and Q and d₂ distance between Q and R as:
d₁ = √ (7-3)² + ( 29-14)²
d₁ = √ 16 + 225
d₂ = √ (11 - 7)² + ( 44 - 29)²
d₂ = √ 16 + 225
If the measure of 1 is 50 degrees what is the measure of 2 ?
Answer:
100
Step-by-step explanation:
if 1 is 50 then the measure of 2 would be 100
Answer:
The measure of angle 2 is
Step-by-step explanation:
angle 1 is 50 degrees and it creates a linear pair (adds up to 180) with the angle right under it.
so we can say that 50+x=180 (x represents angle 2)
subtract x from both sides , 50-50+x=180-50
x= 130
what is 12÷ 1 1/5 = nnnnnn
Rewrite 1 1/5 as 6/5
Now you have 12 / 6/5
When dividing by a fraction, flip the fraction over and multiply:
12 / 6/5 = (12 x 5) /6 = 60/6 = 10
The answer is 10
Answer:
8
Step-by-step explanation:
A journalist interviews 123 people after they leave a restaurant and asks them how confident they are that the food is safe.
Answer:
what do I need to do to answer
Step-by-step explanation:
Find the sum. Express the answer in scientific notation.
(8.7 x 10°)+(4.58 x 10')
O 1.328x108
1.328 x 1010
13.28 x 10°
13.28 x 1018
Answer: A
Step-by-step explanation:
The sum of [tex]8.7 \times 10^9[/tex] and [tex]4.58 \times 10^9[/tex] in scientific notation is [tex]13.28 \times 10^9[/tex].
To find the sum of [tex](8.7 \times 10^9)[/tex] and [tex](4.58 \times 10^9)[/tex] and express it in scientific notation.
we need to add the coefficients and keep the same exponent.
[tex]8.7 \times 10^9 + 4.58 \times 10^9[/tex]
[tex]= (8.7+4.58)\times 10^9[/tex]
[tex]= 13.28 \times 10^9[/tex]
Therefore, the sum of [tex]8.7 \times 10^9[/tex] and [tex]4.58 \times 10^9[/tex] in scientific notation is [tex]13.28 \times 10^9[/tex].
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Complete question:
Find the sum. Express the answer in scientific notation.
(8.7 x 10⁹)+(4.58 x 10⁹)
1.328x10⁸
1.328 x 10¹⁰
13.28 x 10⁹
13.28 x 10¹⁸
I need help with this one
Answer:
The first three
Step-by-step explanation:
I need help with Number 7 please!!!
Answer:
8.06 ft or [tex]\sqrt{65}[/tex] ft
Step-by-step explanation:
Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex] ft per side. This can be approximated to 8.06 ft.
The grades received by 200 students follow a normal distribution. The mean of the grades is 70%, and the standard deviation is 7%.
The number of students who received a grade greater than 70% is about
, and the number of students who got a grade higher than 84% is about
.
Answer:
(5,100)
Step-by-step explanation:
Given that a=4,b=2 and c=-1, find the value of a-b+c
Answer:
1
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
Step 1: Define
a - b + c
a = 4
b = 2
c = -1
Step 2: Solve
Substitute: 4 - 2 - 1Subtract: 2 - 1Subtract: 1Find the value of the expression:
70–a2 for a=–25; 1; 10
Simple answer.
You will have to replace a, with the given numbers.
For the 1st one)
70-25² since a=25. 70-625=-55
2nd)
70-1²=70-1=69
3d)
70-10²=70-100=-30
Hope this helped.
PLEASE HELPPPPPP
the side length of the base of a rectangular prism with a height of 18 inches can be found with the equation b=(v/18)^1/2 v is the volume of the prism find the side length of the base of the volume of the prism is 4050 cubic meters
Answer:
15 if b is supposed to the side length, √15 if b is the base which is a square.
Step-by-step explanation:
Find the number of units x that produces the minimum average cost per unit C in the given equation. C = 0.001x3 + 5x + 250
Answer:
50 units
Step-by-step explanation:
Find the number of units x that produces the minimum average cost per unit C in the given equation.
C = 0.001x³ + 5x + 250
unit cost f(x) = C/x
= 0.001x³/x + 5x/x+ 250/x
f(x) = 0.001x² + 5 + 250/x
f'(x) = 0.002x - 250/x²
We equate the first derivative to zero
0.002x - 250/x² = 0
0.002x = 250/x²
Cross Multiply
0.002x × x² = 250
0.002x³ = 250
x³ = 250/0.002
x³ = 125000
x = 3√(125000)
x = 50 units
Therefore, the number of units x that produces the minimum average cost per unit C is 50 units.
Is 18.18 rational or irrational
Answer:
Rational
Step-by-step explanation:
You are able to put 18.18 in a fraction.
Hope this helped, Have an AMAZING day/night!
9+3 sayısının doğru cevabı kaçtır
What is the correct answer to 9 + 3?
12